This article mainly deals with observer-based H_∞ control problem for a stochastic Korteweg–de Vries–Burgers equation under point or averaged measurements. Due to the nonlinearity of the stochastic partial differential equations, special emphases are given to computation complexity. By constructing an appropriate Lyapunov functional, we derive sufficient conditions in terms of linear matrix inequalities to guarantee the internal exponential stability and H_∞ performance of the perturbed closed-loop system by means of the Lyapunov approach. Consistent simulation results that support the proposed theoretical statements are provided. Finally, we have made important instructions for future research directions.

中文翻译：

---

基于观察者的 H∞ 控制随机 Korteweg-de Vries-Burgers 方程

本文主要研究点或平均测量下随机 Korteweg-de Vries-Burgers 方程的基于观测器的H _∞控制问题。由于随机偏微分方程的非线性，特别强调计算复杂度。通过构造合适的李雅普诺夫泛函，我们在线性矩阵不等式方面推导出充分条件，以通过李雅普诺夫方法保证微扰闭环系统的内部指数稳定性和H _∞性能。提供了支持所提出的理论陈述的一致仿真结果。最后，我们对未来的研究方向做出了重要指示。